I. To acquire a good knowledge of the theory for series and sequences of functions in R.
II. To develop and acquire the methods in the theory of continuous and regular functions in several real variables.
II. To develop and acquire the methods in the theory of continuous and regular functions in several real variables.
Curriculum
scheda docente
materiale didattico
Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.
Programma
Sequences and Series of Functions: Uniform and Total Pointwise Convergence, Limit Passage in the Integral and Derivative, Uniform Convergence Criteria. Power Series and Analytic Functions. Matrix Exponential. Fourier Series: Basic Definitions, Bessel's Inequality, Riemann-Lebesgue Lemma. Pointwise Convergence of the Fourier Series for Piecewise Regular Functions.Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.
Testi Adottati
Analisi Matematica II, Giusti - Analisi Matematica II, ChierchiaBibliografia Di Riferimento
Analisi Matematica II, Giusti - Analisi Matematica II, Chierchia, Marcellini Fusco Sbordone, Analisi IIModalità Frequenza
following the lectures is highly reccommendedModalità Valutazione
The exam consists of a written test (which can be replaced by passing two mid-term tests) covering the course topics, and an oral exam.
scheda docente
materiale didattico
Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.
Programma
Sequences and Series of Functions: Uniform and Total Pointwise Convergence, Limit Passage in the Integral and Derivative, Uniform Convergence Criteria. Power Series and Analytic Functions. Matrix Exponential. Fourier Series: Basic Definitions, Bessel's Inequality, Riemann-Lebesgue Lemma. Pointwise Convergence of the Fourier Series for Piecewise Regular Functions.Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.
Testi Adottati
Analisi Matematica II, Giusti - Analisi Matematica II, ChierchiaBibliografia Di Riferimento
Analisi Matematica II, Giusti - Analisi Matematica II, Chierchia, Marcellini Fusco Sbordone, Analisi IIModalità Frequenza
following the lectures is highly reccommendedModalità Valutazione
The exam consists of a written test (which can be replaced by passing two mid-term tests) covering the course topics, and an oral exam.